You need to kill each stage quickly, when you're rising up that "tower" made of all the horribly malformed monsters. Some of them use curative magic on the other parts. When you get to the top part - right before you fight (SPOILER)Kefka - one of the two monsters will use Life3 on the other one if you give it a chance.

The best approach is to learn the weaknesses of each monster, and make a party that's equipped to exploit those weaknesses. Attack fast, but defend too. Use good armour, protective magic, and Haste for safety. Keep your magic-users on the back row, and have your strongest, best-armed fighters up front.

Hmm. There are probably some good walkthroughs available that can explain it all much better than I can... but good luck!